SYDNEY–Australian politician Tony Abbott has discovered the pitfalls of picking music to support his campaign to become prime minister. This time the musician involved is pop star Katy Perry.

In a radio interview with Ms. Perry, Mr. Abbott’s wish to use her smash hit “Hot N Cold” fell on deaf ears after she switched the debate to his stance on same-sex marriage instead.

In the exchange, the leader of the center-right Liberal-National coalition mused how he liked the tune—a chart topper in countries ranging from Canada to Switzerland— when he first heard it. “I just thought, well, maybe that can be my anthem,” he said on radio station 2day FM.

She also queried how suitable her music might be for a political campaign. “I don’t know if that’s the best song… for a politician,” she said.

Mr. Abbott, who heads the opposition in the Australian House of Representatives, has come under fire for his opposition to gay marriage even though his openly gay sister advocates for the laws to be changed. Prime Minister Kevin Rudd has promised to seek a law change within the first 100 days of his new term, if he is re-elected. Mr. Abbott is favorite to win the Sept. 7 election.

Despite their differences, though, Ms. Perry said she wants to meet Mr. Abbott and his three daughters for lunch when she next visits Australia. “I love you as a human being but I can’t give you my vote,” Ms. Perry told Mr. Abbott.

At a later press conference, Mr. Abbott appeared to live up to the lyrics of “Hot N Cold” by backing away from using Ms. Perry’s tune.

“I was making a light hearted remark about how Katy’s songs are given this kind of relevance, even for Australian politicians, but no – it’s a catchy tune and there are some interesting lyrics,” he told reporters.

Mr. Abbott isn’t the first political leader to run into trouble over music. In 2008, Barack Obama used R&B duo Sam & Dave’s tune “Hold On, I’m Comin” on the presidential campaign trail until singer Sam Moore asked him to stop. And in 2010, the UK Conservative party drew opprobrium from drummer Richard Hughes of the pop group Keane after using their hit single “Everybody’s Changing.”

Even further back, Ronald Reagan in 1984 invoked “the message of hope of a man so many young Americans admire — New Jersey’s own, Bruce Springsteen.” The comments in a speech were an apparent reference to “Born in the U.S.A.,” and Mr. Springsteen didn’t appreciate the plug.

The spotlight on Mr. Abbott comes amid a campaign that has been dominated by perceived gaffes, or political slip ups. Mr. Abbott was criticized Thursday after saying he wouldn’t change his views on gay marriage “based on the fashion of the moment.”

That remark came a day after he described Liberal Party candidate Fiona Scott as having “sex appeal,” a remark that infuriated some, and followed a mistake Monday when he said nobody is “the suppository of all wisdom”.

The opposition leader, who prides himself on a machismo image and muscles honed by triathlon competitions, is sensitive to accusations of sexism. Ousted Prime Minister Julia Gillard drew global attention in 2012 when she accused Mr. Abbott of misogyny in a speech that went viral on the internet.

Mr. Abbott denied the charge and regularly uses his three daughters on the campaign trail to fend off critics.